Uniform error estimates of finite element method for a 3D semilinear elliptic problem with small viscosity

A finite element method based on P1-element for the 3D semilinear elliptic boundary value problem with small viscosity is considered. The existence, uniqueness and uniform optimal H1 and suboptimal L2 error estimates of the finite element solution are provided, where 0<ν<<1≤β. Also, the numerical tests are made to show the efficiency of the error estimates of the finite element solution for the 3D semilinear elliptic boundary value problem with small viscosity.